To determine if 35 is a perfect square, we need to see if there is an integer \( n \) such that \( n^2 = 35 \).
We can start by estimating the square root of 35. The square root of a perfect square is always an integer, so we can check the integers around the approximate square root:
- \( 5^2 = 25 \)
- \( 6^2 = 36 \)
Since \( 5^2 = 25 < 35 < 36 = 6^2 \), we see that the integer values \( 5 \) and \( 6 \) do not yield a perfect square that equals 35.
Additionally, the exact value of \( \sqrt{35} \) is approximately \( 5.916 \), which is not an integer.
Since no integer \( n \) exists such that \( n^2 = 35 \), we conclude that 35 is not a perfect square.
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